Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework, and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of the dielectric decrement of ionic solutions as the ionic concentration increases. We describe the effect of pairs on the Debye screening length, and relate our results to recent surface-force experiments. Furthermore, we show that Bjerrum pairs reduce the ionic concentration in bulk electrolyte and at the proximity of charged surfaces, while they enhance the attraction between oppositely charged surfaces.
We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary reference fluid system. We obtain a modified Poisson-Boltzmann equation as the Euler-Lagrange equation for the obtained functional. Applying Noether's theorem to this functional, we derive a general mean-field expression for the stress tensor consistent with the respective modified Poisson-Boltzmann equation. We derive a general expression for the macroscopic force…
Surface Charge Doping for Ion-Pairing Criticality in Confined Electrolytes
Southern University of Science and Technology（南方科技大学）；Shenzhen Municipal Key-Lab for Advanced Quantum Materials and Devices, and Guangdong Provincial Key Lab for Computational Science and Materials Design, Southern University of Science and Technology（南方科技大学深圳市先进量子材料与器件重点实验室、广东省计算科学与材料设计重点实验室）
The Poisson-Boltzmann (PB) theory is one of the most important theoretical models describing charged systems continuously. However, it suffers from neglecting ion correlations, which hinders its applicability to more general charged systems other than extremely dilute ones. Therefore, some modified versions of the PB theory are developed to effectively include ion correlations. Focused on their applications to ionic solutions, the original PB theory and its variances, including the field-theoretic approach, the correlation-enhanced PB model, the Outhwaite-Bhuiyan modified PB theory and the mea…
Ionic microgels are soft colloidal particles, composed of crosslinked polymer networks, that ionize and swell when dispersed in a good solvent. Swelling of these permeable, compressible particles involves a balance of electrostatic, elastic, and mixing contributions to the single-particle osmotic pressure. The electrostatic contribution depends on the distributions of mobile counterions and coions and of fixed charge on the polymers. Within the cell model, we employ two complementary methods to derive the electrostatic osmotic pressure of ionic microgels. In Poisson-Boltzmann (PB) theory, we m…
The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems. As a mean-field theory, the PB theory neglects the correlation effect in the ionic atmosphere and leads to deviations from experimental results as the concentration or charge valance increases. A modified PB theory including ion correlation effect while retaining its simplicity is critical for many important applications in which ion correlation effect can be significant. In this paper, we present a new model to incorporate ion correlations into the original PB equation by utilizing the Green's function with a non-linear…
The Jones-Ray effect is an anomalous minimum in the surface tension of aqueous electrolytes at millimolar salt concentrations. We experimentally demonstrated that intentionally added ionic surfactants induce the Jones-Ray effect. The one-dimensional Poisson-Boltzmann theory, including the effect of surfactant adsorption and salt depletion, excellently agrees with the obtained experimental data. All the parameters of the ion-specific surface affinities used in the theory are consistent with previous experiments. These results strongly suggest that the Jones-Ray effect observed so far has been i…
The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper we study two such possible sources: long-range Coulombic correlations and solvent excluded volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. W…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform dielectric body. Writing the electrostatic interactions as an integral over electric field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua (Arch. Ratio…
The effects of ionic valency and size asymmetry on counterion adsorption
School of Physics and Astronomy, Tel Aviv University（特拉维夫大学物理与天文学学院）；Center for Physics and Chemistry of Living Systems, Tel Aviv University（特拉维夫大学生物系统物理与化学中心）；School of Chemistry, Tel Aviv University（特拉维夫大学化学学院）；School of Physical Sciences and Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学与柯夫利理论科学研究所）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）；CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所软物质物理重点实验室）
The properties of ionic solutions between charged surfaces are often studied within the Poisson-Boltzmann framework, by finding the electrostatic potential profile. For example, the osmotic pressure between two charged planar surfaces can be evaluated by solving coupled equations for the electrostatic potential and osmotic pressure. Such a solution relies on symmetry arguments and is restricted to either equally or oppositely charged surfaces. Here, we provide a different and more efficient scheme to derive the osmotic pressure straight-forwardly, without the need to find the electrostatic pot…
Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-ener…
In this paper, we explore the effect of a finite surface charge mobility on the interfacial transport: conductance, streaming currents, electro- and diffusio-osmotic flows. We first show that the surface charge mobility modifies the hydrodynamic boundary condition for the fluid, which introduces a supplementary term depending on the applied electric field. In particular, the resulting slip length is found to decrease inversely with the surface charge. We then derive expressions for the various transport mobilities, high-lighting that the surface charge mobility merely moderates the amplificati…
Dielectric permittivity of water confined in stacks of charged lipid layers: extracting profiles from molecular dynamics simulations using a modified Poisson-Boltzmann equation
Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学，法国国家科学研究中心，光物质研究所）；UPR 22/CNRS, Institut Charles Sadron, Université de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心查尔斯·萨德龙研究所）
A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field ({\it e. g.}, Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simp…
The description of a conducting medium in thermal equilibrium, such as an electrolyte solution or a plasma, involves nonlinear electrostatics, a subject rarely discussed in the standard electricity and magnetism textbooks. We consider in detail the case of the electrostatic double layer formed by an electrolyte solution near a uniformly charged wall, and we use mean-field or Poisson-Boltzmann (PB) theory to calculate the mean electrostatic potential and the mean ion concentrations, as functions of distance from the wall. PB theory is developed from the Gibbs variational principle for thermal e…
The standard model for diffuse charge phenomena in colloid science, electrokinetics and biology is the Poisson-Boltzmann mean-field theory, which breaks down for multivalent ions and large surface charge densities due to electrostatic correlations. In this paper, we formulate a predictive continuum theory of correlated electrolytes based on two extensions of the Bazant-Storey-Kornyshev (BSK) framework: (i) a physical boundary condition enforcing continuity of the Maxwell stress at a charged interface, which upholds the Contact Theorem for dilute primitive-model electrolytes, and (ii) scaling r…
We propose a Poisson-Bikerman (PBik) formula for calculating the differential capacitance (DC) of electrical double layers (EDLs) in aqueous electrolytes or ionic liquids. The PBik theory is a generalization of the classical Poisson-Boltzmann theory to include different steric energies of different-sized ions and water similar to different electrical energies for different-charged ions. Water and ions with interstitial voids in this molecular mean field theory have their physical volumes as they do in molecular dynamics simulations. The PBik formula derived from Fermi distributions of ions and…
